CAT 2025 Question Paper | Quant Slot 2

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 9 : Suppose \( a , b , c \) are three distinct natural numbers, such that \( 3 a c = 8 ( a + b ) \). Then, the smallest possible value of \( 3 a + 2 b + c \) is

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Video Explanation

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Explanatory Answer

Rearrange equation for natural numbers

\(3ac=8a+8b\)
\(\Rightarrow b=\frac{3ac-8a}{8}=\frac{a(3c-8)}{8}\)

Test smallest valid integer values for \(a,b,c\)

Since \(a,b,c\) are positive distinct integers:
Try \(c=4\):
\(b=\frac{a(12-8)}{8}=\frac{4a}{8}=\frac{a}{2}\)

Let \(a=2\Rightarrow b=1\).

Checking distinctness: \(a=2,\ b=1,\ c=4\) (all distinct natural numbers).

Compute \(3a+2b+c\)
\(=3(2)+2(1)+4\)
\(=6+2+4=12\)

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The question is " Suppose \( a , b , c \) are three distinct natural numbers, such that \( 3 a c = 8 ( a + b ) \). Then, the smallest possible value of \( 3 a + 2 b + c \) is "

Hence, the answer is '12'

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